The infimum limit, also called the limit inferior or lower limit, of a sequence of real
numbers 
,
written 
and pronounced 'lim-inf,' is the limit of
 |
as 
. Note that by definition,
is nondecreasing and therefore has
a limit in the affinely
extended real numbers. For example, suppose 
, then for 
odd, 
, and for 
even, 
. Another example is 
, in which case 
is a constant sequence 
.
When 
and the common value is finite, the sequence
converges to the real number
 |
Otherwise, the sequence does not converge.
